On a slightly different note: this isn't a good metric. It's a metric of how "balanced" the company is, not the management overhead. If you imagine a company with 150000 engineers and one salesperson, with sales reporting directly to the CEO, hiring more people under the sales director will decrease this metric, while increasing the mean org depth. That probably doesn't measure what you want it to.
> In fact this would be a good metric:
On a slightly different note: this isn't a good metric. It's a metric of how "balanced" the company is, not the management overhead. If you imagine a company with 150000 engineers and one salesperson, with sales reporting directly to the CEO, hiring more people under the sales director will decrease this metric, while increasing the mean org depth. That probably doesn't measure what you want it to.